What is (\partial)/(\partial x)(x/(y^2)+xy+8) ?

The answer to (\partial)/(\partial x)(x/(y^2)+xy+8) is y+1/(y^2)

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(\partial)/(\partial x)(x/(y^2)+xy+8)

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} + x y + 8)

y + \frac{1}{y ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} + x y + 8)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (\frac{x}{y ^{2}}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (8)

\frac{\partial}{\partial x} (\frac{x}{y ^{2}}) = \frac{1}{y ^{2}}

\frac{\partial}{\partial x} (x y) = y

\frac{\partial}{\partial x} (8) = 0

= \frac{1}{y ^{2}} + y + 0

Simplify

= y + \frac{1}{y ^{2}}

\frac{d}{d x} (ln (\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}))

z (z + 1) e^{z}

f (x) = 16 - x^{2}, (1, 4)

\frac{\partial}{\partial x} ((2 x y - 1) e^{- x y})

\frac{d}{d x} (e^{2 (x - 1)^{2}} + \frac{x}{1 + x ^{3}})

What is (\partial)/(\partial x)(x/(y^2)+xy+8) ?
The answer to (\partial)/(\partial x)(x/(y^2)+xy+8) is y+1/(y^2)